Modulational instability of fast magnetosonic waves emitted from a pinching current sheet

We investigate how fast magnetosonic waves can be produced from a pinching current sheet, by using 3-D MHD code. We show that after magnetic pinch of the current sheet due to pressure imbalance, the current sheet begins to expand by an excess of plasma pressure at the center of the current sheet. During the expansion phase, strong fast magnetosonic waves can be created at the steep region of the density gradient and propagate away from the current sheet. It is shown that the fast magnetosonic waves become unstable against modulational instability, as found by Sakai (1983). After the emission of the fast magnetosonic waves, the current sheet will relax to a new equilibrium state, where the current sheet can be heated by adiabatic compression. The emission processes of the fast magnetosonic waves from the current sheet, as well as the modulational instability of these waves that can lead to effective plasma heating through the Landau damping of the slow waves, are important for an understanding of coronal heating and coronal transient brightening.     

Dynamical model of prominence formation and oscillation,I

We investigate a dynamical model of prominence formation in a current sheet at the boundary between two regions of opposite magnetic polarity. Coupled nonlinear equations describing the temporal compression and condensation of plasma in the current sheet are set up as a natural extension of the usual equations for current sheet collapse (Imshennik and Syrovatskii, 1967). It is shown that under certain conditions the current sheet undergoes a nonlinear oscillation during the compression. The thermal instability with cooling is driven by a density enhancement produced during the current sheet formation stage.     

Non-linear tearing structures in equilibrium current sheet

A family of exact analytic solutions of the time-independent Vlasov-Maxwell equations is presented. The solutions describe two-dimensional equilibrium current sheet with magnetic field structures resembling that produced by the tearing instability. In particular, the solutions presented here do not restrict the field in the magnetic island to small magnitude. It is shown that as the scale length of the magnetic island increases, the thickness of the current sheet increases while the average current and the average magnetic energy decrease. The tearing structures described by the solutions may exist in the magnetotail current sheet, the magnetopause current layer and the field-aligned auroral sheet current.     

The warm current sheet model, and its implications on the temporal behaviour of the geomagnetic tail

A simple model current sheet is studied numerically. Consistent fields and particle trajectories, and their dependence on electron and proton temperature, convection velocity and normal field, B_z, linking through the current sheet, are presented and discussed. It is shown that the protons, which are the major current carriers, largely retain the decoupling of the motion in the x-y plane from the normal oscillations as in the ‘cold’ current sheet. The positive potential of the current sheet is shown to be sufficient to trap some energetic electrons, the motion of which enables the predominance of energetic electrons towards the dawn side of the tail to be understood. Semi-empirical relationships for the thickness and the potential of the current sheet are obtained.

The consequences of such a current sheet on the behaviour of the geomagnetic tail are investigated. Using Faraday's law and the consistent cross tail electric field it is shown that the effect of a southward turning of the interplanetary field is to lead to a decrease in B_z,an increase of the current sheet conductivity, and a growth of stored field energy, i.e. the current sheet blocks merging. The decrease of the resistance of the current sheet is limited by the finite width of the tail. Finally, it is pointed out that if the conditions which bring about the growth of field energy persist, then the collapse of the field lines characteristic of substorms may occur.     

太阳爆发过程中的大尺度磁重联电流片:理论和观测

从理论和观测两个方面来介绍和讨论出现在太阳爆发过程中的磁重联电流片及其物理本质和动力学特征。首先介绍在理论研究和理论模型中,磁重联电流片是如何在爆发磁结构当中形成并发展的,对观测研究有什么指导意义。然后介绍观测工作是从哪几个方面对理论模型预测的电流片进行证认和研究的。第三,将介绍观测研究给出了哪些过去所没有能够预期的结果,这些结果对深入研究耀斑一CME电流片以及其中的磁重联过程的理论工作有什么重要的、挑战性的意义。第四,讨论最新的与此有关的理论研究和数值实验。最后,对未来的研究方向和重要课题进行综述和展望。     

Excitation of an electrostatic wave by a cold electron current sheet of finite thickness

Electrostatic waves excited by a field-aligned electron current sheet of finite thickness are investigated. The finite width of the current sheet gives rise to boundary conditions to be satisfied at the sheet edge. This results in a restriction to the number of modes which may be driven unstable. Ducted and evanescent mode solutions are obtained. It is shown that the finite thickness of the current sheet partially stabilizes the system and contributes to the coherence of the excited waves.     

Modelling heliospheric current sheet drift in stochastic cosmic ray transport models

Drifts are one of the major cosmic ray modulation mechanisms in the heliosphere. Three types of drifts occur in the background heliospheric magnetic field, namely curvature, gradient and current sheet drifts. The last component occurs because of the switch in magnetic field polarity across the heliospheric current sheet and is the main topic of study. We discuss and implement a new approach to model drifts in a numerical modulation model. The model employs stochastic differential equations to solve the relevant transport equation in five (three spatial, energy and time) dimensions. What is of interest is the fact that the model can handle current sheet tilt angles up to the theoretical maximum of α=90° and still remain numerically stable. We use the additional insights gained from the numerical model to investigate the effectiveness of drifts along the current sheet by examining the relationship between the current sheet path length and the cosmic ray propagation time. It is found that diffusion can disrupt the drift process very effectively, leading to diffusive short circuiting of the current sheet by the cosmic rays.     

The analytic properties of the flapping current sheets in the earth magnetotail

The current sheet in Earth’s magnetotail often flaps, and the flapping waves could be induced propagating towards the dawn and dusk flanks, which could make the current sheet dynamic. To explore the dynamic characteristics of current sheet associated with the flapping motion holistically and provide reasonable physical interpretations, detailed direct calculation and analysis have been applied to one approximate analytic model of magnetic field in the flapping current sheet. The main results from the model demonstrate: (1) the magnetic fluctuation amplitude is attenuated from the center of current sheet to the lobe regions; The larger wave amplitude would induce the larger magnetic amplitude; (2) the curvature of magnetic field lines (MFLs), with maximum at the center of current sheet, is only dependent on the displacement Z along the south-north direction from the center of current sheet, regardless of the tilt of current sheet; (3) the half-thickness of neutral sheet, h, the minimum curvature radius of MFLs, R_cmin, and the tilt angle of current sheet, δ, satisfies h=R_cmin cos δ; (4) the gradient of magnetic strength forms a double-peak profile, and the peak value would be more intense if the local current sheet is more tilted; (5) current density j and its j_y, j_z components reach the extremum at the center of CS. j and j_z would be more intense if the local current sheet is more tilted, but it is not the case for j_y; and (6) the field-aligned component of current density mainly appears in the neutral sheet, and the sign of it would change alternatively as the flapping waves passing by. To check the validity of the model, one simulation on the virtual measurements has been made, and the results are in well consistence with actual observations of Cluster.     

Generalized analytical models of Syrovatskii’s current sheet

Two-dimensional stationary magnetic reconnection models that include a thin Syrovatskii-type current sheet and four discontinuous magnetohydrodynamic flows of finite length attached to its endpoints are considered. The flow pattern is not specified but is determined from a self-consistent solution of the problem in the approximation of a strong magnetic field. Generalized analytical solutions that take into account the possibility of a current sheet discontinuity in the region of anomalous plasma resistivity have been found. The global structure of the magnetic field in the reconnection region and its local properties near the current sheet and attached discontinuities are studied. In the reconnection regime in which reverse currents are present in the current sheet, the attached discontinuities are trans-Alfvénic shock waves near the current sheet endpoints. Two types of transitions from nonevolutionary shocks to evolutionary ones along discontinuous flows are shown to be possible, depending on the geometrical model parameters. The relationship between the results obtained and numerical magnetic reconnection experiments is discussed.     

Consistency of fields and particle motion in the ‘Speiser’ model of the current sheet

The consistency between fields and particle motion in the region of the current sheet where the field lines link through the current sheet has been investigated.     

Coupled guided modes in the magnetotails: spatial structure and ballooning instability

The problem of the spatial structure of coupled azimuthally small-scale Alfvén and slow magnetosonic (SMS) waves is solved in an axisymmetric magnetotail model with a current sheet. It is shown that the linear transformation of these waves occurs in the current sheet on magnetic field lines stretched into the magnetotail. From the ionosphere to the current sheet these modes are linearly independent. Due to the high ionospheric conductivity the structure of coupled modes along magnetic field lines represents standing waves with very different typical scales in different parts of the field line. In most of the field line their structure is determined by the large-scale Alfvén wave structure. Near the ionosphere and in the current sheet, small-scale SMS wave field starts to dominate. In these regions coupled modes becomes small-scale. Such modes are neutrally stable on the field lines that do not cross the current sheet, but switch to the ballooning instability regime on field lines crossing the current sheet. An external source is required to generate these modes and this paper considers external currents in the ionosphere as a possible driver. In the direction across magnetic shells the coupled modes are waves running away from the magnetic shell on which they were generated.     

Non-evolutionarity of a reconnecting current sheet as a cause of its splitting into MHD shocks

Numerical simulations of the magnetic reconnection process in a current sheet show that, in some cases, MHD shocks appear to be attached to edges of the sheet. The appearance of the shocks may be considered to be a result of splitting of the sheet. In the present paper we suppose that this splitting takes place in consequence of non-evolutionarity of the reconnecting current sheet as a discontinuity. The problem of time evolution of small perturbations does not have a unique solution for a non-evolutionary discontinuity, and it splits into other (evolutionary) discontinuities. Such an approach allows us to determine conditions under which the splitting of the-sheet occurs. The main difficulty of this approach is that a current sheet is not reduced to a classified 1D discontinuity, because inhomogeneity of flow velocity inside the sheet is two-dimensional. To formulate the non-evolutionarity problem, we solve the linear MHD equations inside and outside the sheet and deduce linearized 1D boundary conditions at its surface. We show that for large enough conductivity, small perturbations exist which interact with the sheet as with a discontinuity. Then we obtain a non-evolutionarity criterion, with respect to these perturbations, in the form of a restriction on the flow velocity across the surface of the sheet.     

A note on the motion of charged particles in one-dimensional magnetic current sheets

By considering the integrals of the motion of charged particles moving in one-dimensional current sheets, a simple and exact proof is given that particles which are either magnetically or electrostatically trapped about such a current sheet exhibit zero net drift. The transition to the special case of a strictly neutral sheet, a limit remaining unclear from previous studies, is also elucidated. Finally, the relationship between the results and existing self-consistent current sheet solutions is discussed.     

Laboratory simulation of energy release in solar flares

A laboratory simulation method is proposed for energy release processes occurring in a fragment of the flare current sheet on the Sun. The method relies on the assumption that the spatial scale of such processes is represented by the current sheet's thickness whose values can be close for both the solar and laboratory conditions. It is shown that in an extended current sheet, current dissipation on anomalous resistivity that ensures the specific power of energy release close to that observed in a flare, is the main energy release mechanism. A rapid compression of the sheet by external magnetic fields can provide the condition for switching on a powerful energy release. The tearing instability developing in a homogeneous neutral sheet, leads to the formation of magnetic islands in which the energy release is localized.     

Structure of the Jovian magnetodisk current sheet:: initial Galileo observations

The ten-degree tilt of the Jovian magnetic dipole causes the magnetic equator to move back and forth across Jupiters rotational equator and the Galileo orbit that lies therein. Beyond about 24 Jovian radii, the equatorial current sheet thins and the magnetic structure changes from quasi-dipolar into magnetodisk-like with two regions of nearly radial but antiparallel magnetic field separated by a strong current layer. The magnetic field at the center of the current sheet is very weak in this region. Herein we examine the current sheet at radial distances from 24–55 Jovian radii. We find that the magnetic structure very much resembles the structure seen at planetary magnetopause and tail current sheet crossings. The magnetic field variation is mainly linear with little rotation of the field direction. At times there is almost no small-scale structure present and the normal component of the magnetic field is almost constant through the current sheet. At other times there are strong small-scale structures present in both the southward and northward directions. This small-scale structure appears to grow with radial distance and may provide the seeds for the explosive reconnection observed at even greater radial distances on the nightside. Beyond about 40 Jovian radii, the thin current sheet also appears to be almost constantly in oscillatory motion with periods of about 10 min. The amplitude of these oscillations also appears to grow with radial distance. The source of these fluctuations may be dynamical events in the more distant magnetodisk.     

Thermal trigger for solar flares and coronal loops formation

A longitudinal stability is considered for the quasi-steady current sheet which is uniform along the current. In the MHD approximation, the stability problem is solved for the plane neutral sheet and small disturbances propagating along the current. The current sheet is shown to break-up into the system of cooler and more dense filaments due to radiative cooling. The filaments are parallel to magnetic field lines. This process corresponds to the condensation mode of a thermal instability and can play a trigger role for a solar flare. Moreover, at the nonlinear stage of development, it can lead to the formation of very dense cold filaments surrounded by high-temperature low-density plasma inside the current sheet. Flowing into the filaments, hot plasma is cooled by radiation and compressed. Then the cold dense plasma flows out from the current sheet along the filaments. We think that the process under consideration is responsible for the often observed picture of an arcade of cold loops in the solar corona.The text of this paper was written by B. V. Somov after the death of Prof. S. I. Syrovatskii.     

Observing the reconnection region in a transequatorial loop system

A vertical current sheet is a crucial element in many flare/coronal mass ejection (CME) models. For the first time, Liu et al. reported a vertical current sheet directly imaged during the flare rising phase with the EUV Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO). As a follow-up study, here we present the comprehensive analysis and detailed physical interpretation of the observation. The current sheet formed due to the gradual rise of a transequatorial loop system. As the l...     

A 2-D model for the support of a polar-crown solar prominence

We present a 2-D potential-field model for the magnetic structure in the environment of a typical quiescent polar-crown prominence. The field is computed using the general method of Titov (1992) in which a curved current sheet, representing the prominence, is supported in equilibrium by upwardly directed Lorentz forces to balance the prominence weight. The mass density of the prominence sheet is computed in this solution using a simple force balance and observed values of the photospheric and prominence magnetic field. This calculation gives a mass density of the correct order of magnitude. The prominence sheet is surrounded by an inverse-polarity field configuration adjacent to a region of vertical, open polar field in agreement with observations.A perturbation analysis provides a method for studying the evolution of the current sheet as the parameters of the system are varied together with an examination of the splitting of an X-type neutral point into a current sheet.Program Systems Institute of the Russian Academy of Sciences, Pereslavl-Zalessky 152140, Russia.     

Stability of Current Sheets in the Solar Corona

This work aims at investigating unstable modes of oscillation of quasi-vertical two-dimensional current sheets with sheared magnetic fields under physical conditions typical for the solar corona. We use linear magnetohydrodynamic equations to obtain sets of unstable modes related to the longitudinal inhomogeneity of the current sheet. It is shown that these modes of current sheet oscillations can modulate the current sheet thickness along the polarity inversion line. Based on the obtained results, we propose a scenario which can naturally explain both the quasi-periodic pulsations of hard X-ray emission and the parallel movement of their double footpoint-like sources along the polarity inversion line observed in some eruptive two-ribbon solar flares.     

Some properties of the current sheet in the geomagnetic tail

The topic of this report is that of the influence of noise, and of the finite length and width of the tail on the behaviour of the current sheet.The presence of a weak magnetic field linking through the current sheet leads to plasma containment and counterstreaming, with the consequence that both the plasma temperature and density are increased in the vicinity of the current sheet. The effect of these changes on the relationship between steady bulk parameters is discussed.The finite length of the tail significantly modifies the equilibrium situation in the near Earth tail, for streams mirroring at the Earthwards end of field lines lead to a reduction of merging. The finite width of the tail restricts the region of reduced merging rate to a triangular shaped area extending from the dusk magnetopause into the tail. The finite tail width is also important in the more distant tail, where magnetosheath particles which penetrate the magnetopause ends of the current sheet may become major current carriers, especially if B_z, is small and northwards.Finally, it is shown that the above factors, together with a non-adiabatic current sheet, are important to our understanding of the temporal behaviour of the tail.